Topic 7 Review

Adding, Subtracting, and Naming Polynomials

100

What is the name of this polynomial?

-7x³+9x²+5x-14

Cubic polynomial

200

Write this polynomial in standard form.

7x²-9x-3+x⁴

x⁴+7x²-9x-3

300

Add. Then write the polynomial in standard form.

(5x³-6x²+3x-8)+(3x³-3x²+7x+13)

8x³-9x²+10x+5

400

Subtract. Then write the polynomial in standard for

(2x⁴-4x³+5x²+2x-5)-(2x³-5x²-12x+11)

2x⁴-6x³+10x²+14x-16

500

Subtract. Then write the polynomial in standard form and name it.

(3x⁴+6x³-2x²+8x+4)-(x⁴-3x³+4x²-5x+9)

2x⁴+9x³-6x²+13x-5

4th degree polynomial

Multiplying Polynomials and Special Cases

100

Find the product

(x+5)²

x²+10x+25

200

Find the product. No calculator.

57²

3249

300

Find the product

3x²(2x²-7x+5)

6x⁴-21x³+15x²

400

Find the product

(2x-5)(2x²+8x-9)

4x³+6x²-58x+45

500

A circular flower garden surrounds a sculpture on a square base. The radius of the circle is 5x, and the side length of the square is 3x. What is an expression for the area of the flower garden?

25πx²-9x²

Factoring Polynomials

100

What is the GCF of the terms of this polynomial?

8x²+12

GCF=4

200

What is the GCF

4x²y-16x

4x

300

Factor out the GCF of this polynomial.

6x²-10x-8

2(3x²-5x-4)

400

Factor out the GCF 

3x²-9x+3

3(x²-3x+1)

500

Why are the terms x²+7 said to be relatively prime?

Because they can only be found by multiplying it's self by 1.

Factoring x^2+bx+c and ax^2+bx+c

100

Factor this trinomial

x²+16+64

(x+8)²

200

Factor this

x²+7x+10

(x+2)(x+5)

300

Factor this

27x²-3

3(3x-1)(3x+1)

400

Factor this trinomial

2x²+28+98

2(x+7)²

500

Factor this

49x²-14x+1

(7x-1)(7x-1)

Frame Problems

100

A rectangular picture has a length of x+4 inches. and a width of x inches. A frame adds 2 inches to each side of the picture. What is the area of the frame?

A=64in²

200

You have a square picture with a 3-inch frame around it. If the area of the frame is 108 in², what is the area of the picture?

A=36in²

300

A square picture has a frame 2 inches wide around it. The area of the frame is 60in². What is the area of the picture?

A=30.25in²

400

A rectangular picture has length x+4 and width x+2. A frame 2 inches wide is placed around the picture. Solve for x and find the dimensions.

x=2.5 inches

6.5 inches by 4.5 inches

500

A rectangular picture is x inches by x+6 inches. A frame of uniform width 3 inches is placed around the picture. Write an equation to represent the situation and solve for x. What are the dimensions?

(x+6)(x+12)-x(x+6)

x=9 inches

9 inches x 15 inches